Harmonic Oscillator Research Articles

Two-dimensional solitons in second-harmonic-generating media with fractional diffraction

We introduce a system of propagation equations for the fundamental-frequency (FF) and second-harmonic (SH) waves in the bulk waveguide with the effective fractional diffraction and quadratic (χ(2)) nonlinearity. The numerical solution produces families of ground-state (zero-vorticity) two-dimensional solitons in the free space, which are stable in exact agreement with the Vakhitov–Kolokolov criterion, while vortex solitons are completely unstable in that case. Mobility of the stable solitons and inelastic collisions between them are briefly considered too. In the presence of a harmonic-oscillator (HO) trapping potential, families of partially stable single- and two-color solitons (SH-only or FF-SH ones, respectively) are obtained, with zero and nonzero vorticities. The single- and two-color solitons are linked by a bifurcation which takes place with the increase of the soliton’s power.

Krylov complexity of density matrix operators

Quantifying complexity in quantum systems has witnessed a surge of interest in recent years, with Krylov-based measures such as Krylov complexity (CK) and Spread complexity (CS) gaining prominence. In this study, we investigate their interplay by considering the complexity of states represented by density matrix operators. After setting up the problem, we analyze a handful of analytical and numerical examples spanning generic two-dimensional Hilbert spaces, qubit states, quantum harmonic oscillators, and random matrix theories, uncovering insightful relationships. For generic pure states, our analysis reveals two key findings: (I) a correspondence between moment-generating functions (of Lanczos coefficients) and survival amplitudes, and (II) an early-time equivalence between CK and 2CS. Furthermore, for maximally entangled pure states, we find that the moment-generating function of CK becomes the Spectral Form Factor and, at late-times, CK is simply related to NCS for N ≥ 2 within the N-dimensional Hilbert space. Notably, we confirm that CK = 2CS holds across all times when N = 2. Through the lens of random matrix theories, we also discuss deviations between complexities at intermediate times and highlight subtleties in the averaging approach at the level of the survival amplitude.

Разработка методики диагностирования и определения остаточного ресурса механических демпферов крутильных колебаний машинно-движительных комплексов судов

Import substitution issues in modern conditions remain an urgent topic today, especially in terms of periodic maintenance of mechanical torsional vibration dampers of foreign manufacture (they are also called spring dampers). Diagnostics of such devices is impossible due to the influence of sanctions against Russia, namely, in the absence of the possibility of the arrival of defect specialists from leading specialized organizations and manufacturing plants. A method for developing a model mechanical damper is presented, taking into account all conditions of similarity: geometric, kinematic and dynamic. Through the use of modern Autodesk Fusion 360 software, a digital model of a real Geislinger marine damper model D90/37 (Austria) has been developed. The results of diagnostics of the Kogalym and Langepas ship propulsion systems, which include mechanical dampers, are also reflected, and the dynamics of changes in torsional vibration parameters is analyzed. It is noted that non-selective diagnostics (torsiography procedure) is possible only in coordination with the supervisory authorities, usually with a small operating time of the damper. All further diagnostics are allowed only if there is an approved standard methodology, which currently does not exist, which confirms the relevance of the chosen research topic. An initial version of the methodology for diagnosing and determining the residual life of mechanical torsional vibration dampers of ship propulsion systems is presented.

Metro-induced vibration attenuation using rubberized concrete slab track

This paper addresses two important worldwide environmental concerns: disposal of waste tyres and attenuation of trains induced vibration. To this end, use of the waste materials in construction of railway concrete slabs for reduction of train induced vibration is investigated in this research. For this purpose, rubber tyre particles with different dosages were used in the concrete mixtures of test specimens. Extensive laboratory tests were conducted on the rubberized concrete specimens to measure their compressive strength, density and damping of the specimens. The effect of rubberized slab track on attenuation of vibration propagated from slab track was investigated by numerical modeling using results of laboratory tests as the input data. The laboratory results obtained indicate that adding rubber particles to the railway slab causes up to 96% increase in damping ratio (for concrete with 10% rubber). Results of numerical analysis elucidates that the rubberized slab track causes up to 21% reduction of the train induced vibration. By compromising between compressive strength and damping of vibration, it is shown that the optimum amount of crumb rubber in the concrete of railway slabs is 2.5% by which the best performance of the railway slabs is obtained.

Group‐weighted oscillatory containment for multiple robots under heterogeneous cooperation and competition

AbstractThe group‐weighted containment (GWC) problem is studied for swarms of robots, where the information flow among agents is heterogeneous (weighted) cooperative‐competitive and the whole networked systems are composed of multiple different groups. Each group is formed by multiple harmonic oscillator leaders and multiple robot followers governed by Euler‐Lagrange (EL) equations. After introducing the definition of group‐weighted containment to the networked robot systems, the control algorithms for the agents containing followers and leaders are formulated over newly weighted cooperative‐competitive network. Some necessary conditions for solving the weighted containment control problem are established. It is shown that the followers in every group can achieve a kind of novel coordinated behaviors. Specifically, the followers can converge to the dynamic convex hull spanned by the corresponding leaders' weighted coordinates under some conditions. Simulation results are provided to illustrate the effectiveness of the proposed control schemes.

Preparation and energy absorption of flexible polyurethane foam with hollow glass microsphere

This paper presents the preparation of a partially open-cell and partially closed-cell flexible polyurethane foam material (flex-PUF), which exhibits improved cushioning performance compared to conventional protective materials. Hollow Glass Microspheres (HGM) were used as a filling material to enhance the compressibility of the material. In order to investigate the effects of HGM on the multi-impact protection and vibration damping performance of flex-PUF with different thicknesses, flex-PUF samples filled with varying volume fractions of HGM were subjected to multi-impact testing and dynamic viscoelasticity experiments. The destructive mechanism of HGM under impact was observed using scanning electron microscopy (SEM). The experimental results revealed that, under the same impact energy conditions, filling flex-PUF with HGM reduced the maximum impact displacement while enhancing energy absorption, although at the expense of cushioning performance. As the number of impact increases, the stiffness of flex-PUF decreased. In the vibration experiments, as the frequency increased, the proportion of flex-PUF’s viscous damping energy dissipation decreases.

Anomalous and ultraslow diffusion of a particle driven by power-law-correlated and distributed-order noises

We study the generalised Langevin equation (GLE) approach to anomalous diffusion for a harmonic oscillator and a free particle driven by different forms of internal noises, such as power-law-correlated and distributed-order noises that fulfil generalised versions of the fluctuation-dissipation theorem. The mean squared displacement and the normalised displacement correlation function are derived for the different forms of the friction memory kernel. The corresponding overdamped GLEs for these cases are also investigated. It is shown that such models can be used to describe anomalous diffusion in complex media, giving rise to subdiffusion, superdiffusion, ultraslow diffusion, strong anomaly, and other complex diffusive behaviours.

Noise filtering options for conically scanning Doppler lidar measurements with low pulse accumulation

Abstract. Doppler lidar (DL) applications with a focus on turbulence measurements sometimes require measurement settings with a relatively small number of accumulated pulses per ray in order to achieve high sampling rates. Low pulse accumulation comes at the cost of the quality of DL radial velocity estimates and increases the probability of outliers, also referred to as “bad” estimates or noise. Careful filtering is therefore the first important step in a data processing chain that begins with radial velocity measurements as DL output variables and ends with turbulence variables as the target variable after applying an appropriate retrieval method. It is shown that commonly applied filtering techniques have weaknesses in distinguishing between “good” and “bad” estimates with the sensitivity needed for a turbulence retrieval. For that reason, new ways of noise filtering have been explored, taking into account that the DL background noise can differ from generally assumed white noise. It is shown that the introduction of a new coordinate frame for a graphical representation of DL radial velocities from conical scans offers a different perspective on the data when compared to the well-known velocity–azimuth display (VAD) and thus opens up new possibilities for data analysis and filtering. This new way of displaying DL radial velocities builds on the use of a phase-space perspective. Following the mathematical formalism used to explain a harmonic oscillator, the VAD’s sinusoidal representation of the DL radial velocities is transformed into a circular arrangement. Using this kind of representation of DL measurements, bad estimates can be identified in two different ways: either in a direct way by singular point detection in subsets of radial velocity data grouped in circular rings or indirectly by localizing circular rings with mostly good radial velocity estimates by means of the autocorrelation function. The improved performance of the new filter techniques compared to conventional approaches is demonstrated through both a direct comparison of unfiltered with filtered datasets and a comparison of retrieved turbulence variables with independent measurements.

Highly sensitive and label-free protein immunoassay-based biosensor comprising infrared metamaterial absorber inducing strong coupling

A mid-infrared label-free immunoassay-based biosensor is an effective device to help identify and quantify biomolecules. This biosensor employs a surface-enhanced infrared absorption spectroscopy, which is a highly potent sensing technique for detecting minute quantities of analytes. In this study, a biosensor was constructed using a metamaterial absorber, which facilitated strong coupling effects. For maximum coupling effect, it is necessary to enhance the near-field intensity and the spatial and spectral overlap between the optical cavity resonance and the vibrational mode of the analyte. Due to significant peak splitting, conventional baseline correction methods fail to adequately analyze such a coupling system. Therefore, we employed a coupled harmonic oscillation model to analyze the spectral distortion resulting from the peak splitting induced by the strong coupling effect. The proposed biosensor with a thrombin-binding aptamer-based immunoassay could achieve a limit of detection of 267.4 pM, paving the way for more efficient protein detection in clinical practice.

Vibration assisted electron tunnelling in COVID-19 infection using quantum state diffusion.

The spread of the COVID-19 virus has become a global health crisis, and finding effective treatments and preventions is a top priority. The field of quantum biology primarily focuses on energy or charge transfer, with a particular emphasis on photosynthesis. However, there is evidence to suggest that cellular receptors such as olfactory or neural receptors may also use vibration-assisted electron tunnelling to enhance their functions. Quantum tunnelling has also been observed in enzyme activity, which is relevant to the invasion of host cells by the SARS-CoV-2 virus. Additionally, COVID-19 appears to disrupt receptors such as olfactory receptors. These findings suggest that quantum effects could provide new insights into the mechanisms of biological systems and disease, including potential treatments for COVID-19. We have applied the open quantum system approach using Quantum State Diffusion to solve the non-linear stochastic Schrödinger equation (SSE) for COVID-19 virus infection. Our model includes the mechanism when the spike protein of the virus binds with an ACE2 receptor is considered as dimer. These two entities form a system and then coupled with the cell membrane, which is modelled as a set of harmonic oscillators (bath). By simulating the SSE, we find that there is vibration-assisted electron tunnelling happening in certain biological parameters and coupling regimes. Furthermore, our model contributes to the ongoing research to understand the fundamental nature of virus dynamics. It proposes that vibration-assisted electron tunneling could be a molecular phenomenon that augments the lock-and-key process for olfaction. This insight may enhance our understanding of the underlying mechanisms governing virus-receptor interactions and could potentially lead to the development of novel therapeutic strategies.

Ultra‐Narrow Linewidth Polariton Lasing in Optically Trapped Bose‐Einstein Condensates at Room Temperature

AbstractPolariton lasing via Bose‐Einstein condensation (BEC) provides a peculiar method to achieve low threshold coherent light sources. Until now, the cryogenic operating temperature required for polariton lasers has hampered the development of polaritonics. Here, a novel approach is first reported to realize the ultra‐narrow linewidth polariton lasing under quasi‐3D quantum confinement at room‐temperature (RT). The potential trap landscape is constructed by ring‐shaped optical excitation, wherein the continuum polariton dispersion is modulated into discrete simple harmonic oscillator (SHO) states. The coherent condensation lasing of trapped polaritons occurs beyond the threshold power. Benefiting from the horizontal quantum confinement, the trapped polariton lasing exhibits an ultra‐narrow linewidth (0.7 meV) and excellent quality factor (Q = 3510). Moreover, the second‐order quantum coherence properties of trapped polariton condensation are determined to reveal the quantum phase transition of Bosonic system. The results offer a feasible route for realizing a low‐threshold ultra‐narrow linewidth polariton laser at RT, which significantly facilitates the fabrication of polariton laser and switches on opportunities for future applications.

Monoreactive multimass oscillator of non-fixed frequency

Introduction. The work relates to the field of mechanical engineering, namely to oscillating mechanical systems. The relevance of the study is determined by the fact that vibrations of inertial masses occur everywhere.Target. Development of a mathematical model of a monoreactive multimass oscillator of non-fixed frequency.Research methods. It is proved that the points that are the coordinates of the end of an arbitrary vector in the coordinate system are the vertices of a regular polygon. The shape and dimensions of the polygon are not related to the coordinates of the vector, i.e. unchangeable. The center of a regular polygon in all cases coincides with the middle of the vector. In the considered (idealized) case, the polygon, at the vertices of which oscillating loads of masses m are located, lies in the Z plane. In technical applications, the loads should not interfere with each others movements, therefore, each load should have its own plane, and all planes should be parallel (like multi-piston mechanism).Results. The condition for the occurrence of free harmonic oscillations is the equality to zero of the total energy of the system, which in the case under consideration is exclusively kinetic, which determines the monoreactive nature of the oscillator. In the considered multidimensional flat monoreactive oscillator, free harmonic linear oscillations of weights can occur.Conclusion. Only kinetic energy is involved in energy exchange. There is no need for elastic elements. The oscillator does not have a fixed natural frequency of oscillation. The frequency depends on the initial speeds and positions of the weights. A regular polygon undergoes a double rotation - around point 0 and around point r. At the same time, the loads carry out linear harmonic oscillations with amplitude . The use of a crank-slider or crank-rod mechanism will allow for parallel movement of loads.

Evaluation of the single-frequency variometric approach based on low-cost GNSS observations and different satellite combinations for detecting short-term dynamic behaviors

This study presents the capability of the single-frequency (SF) variometric approach (VA) technique with low-cost GNSS observations to detect short-term dynamic behaviors. Harmonic oscillations with amplitudes between 5 and 20 mm and frequencies between 0.3 and 5.0 Hz were generated employing a single-axis shake table to investigate the performance of the SF-VA technique in the structural health monitoring (SHM) system. Besides, a Mw 6.9 Kobe, 1995 earthquake simulation was generated using the shake table to analyze the SF-VA performance for the earthquake early warning (EEW) system. A low-cost u-blox ZED-F9P GNSS receiver and ANN-MB-00 patch antenna were used to collect GNSS observations at a 20 Hz sampling rate during the experiments. The observations were processed using the MATLAB-based open-source PPPH-VA software in real-time (RT) mode, considering eight different satellite combinations. The capability of the SF-VA technique to detect horizontal dynamic behaviors in RT mode was investigated in the frequency and time domains, accepting the displacements from the linear variable differential transformer sensor as a reference. The results in the frequency domain demonstrate that the SF-VA technique with low-cost GNSS observations can successfully detect the peak frequency value of short-term harmonic oscillations up to 5 Hz. Moreover, time domain findings emphasize that the short-time dynamic oscillations can be determined with the SF-VA technique with an accuracy ranging from 0.8 to 6.4 mm. Earthquake simulation experiment results demonstrate that the strong ground motions caused by mega earthquakes can be determined at mm-level by the SF-VA method. The results of both experiments show that multi-GNSS observations contribute to the SF-VA technique considerably. Overall, the findings reveal that the SHM and EEW systems can be operated with low-cost GNSS receivers, and the natural frequency of the man-made structures and accurate displacement values of seismic waveforms can be determined in RT with the SF-VA technique.

Casimir–Onsager matrix for weakly driven processes

Modeling of physical systems must be based on their suitability to unavoidable physical laws. In this work, in the context of classical, isothermal, finite-time, and weak drivings, I demonstrate that physical systems, driven simultaneously at the same rate in two or more external parameters, must have the Fourier transform of their relaxation functions composing a positive-definite matrix to satisfy the Second Law of Thermodynamics. By evaluating them in the limit of near-to-equilibrium processes, I identify that such coefficients are the Casimir–Onsager ones. The result is verified in paradigmatic models of the overdamped and underdamped white noise Brownian motions. Finally, an extension to thermally isolated systems is made by using the time-averaged Casimir–Onsager matrix, in which the example of the harmonic oscillator is presented.

Damping Optimization Method of Combine Harvester Frame Undergoing Multi-Source Excitation

The complex mechanical system of a rice combine harvester not only has various excitation sources, but also, the vibration transmission path between each working device and the vibration contribution characteristics to the frame are not clear, so it is difficult to perform a reduction vibration design for the sharp vibration of the rice combine harvester frame. Therefore, based on the comparison and improvement of multiple classical transfer path analysis methods, this paper analyzed the vibration transfer characteristics and transfer characteristics of each harvester by the discrete time matrix method and operating path method. In the Experimental section, through the vibration characteristic experiment firstly, this paper obtained the power spectrum variation and the most needed optimized path in the transmission path of each device under each operating condition. Secondly, through frame simulation analysis under the exciting force, we obtained the vibration damping areas that needs to be optimized. Finally, the damping optimization experiment connected with the vibration characteristic experiment, and the excitation force simulation analysis was performed. The results of the damping optimization experiment displayed that the maximum change value of the vibration acceleration of the cutting table decreased from 7.862 m·s−2 to 3.522 m·s−2, decreasing by 55.2%, and the peak amplitude of the multipoint test in the cab was 5.4, 5.3, 1.7 and 2.0 μm, respectively, which was significantly reduced, so the optimization effect was significant. This study provides theoretical support for the vibration reduction optimization of a rice combine harvester frame.

Observation of a phase space horizon with surface gravity water waves

In 1974, Stephen Hawking predicted that quantum effects in the proximity of a black hole lead to the emission of particles and black hole evaporation. At the very heart of this process lies a logarithmic phase singularity which leads to the Bose-Einstein statistics of Hawking radiation. An identical singularity appears in the elementary quantum system of the inverted harmonic oscillator. In this Letter we report the observation of the onset of this logarithmic phase singularity emerging at a horizon in phase space and giving rise to a Fermi-Dirac distribution. For this purpose, we utilize surface gravity water waves and freely propagate an appropriately tailored energy wave function of the inverted harmonic oscillator to reveal the phase space horizon and the intrinsic singularities. Due to the presence of an amplitude singularity in this system, the analogous quantities display a Fermi-Dirac rather than a Bose-Einstein distribution.

Vibratory Conveying by Normal Oscillations with Piecewise Constant Acceleration and Longitudinal Harmonic Oscillations

Vibratory Conveying by Normal Oscillations with Piecewise Constant Acceleration and Longitudinal Harmonic Oscillations

Mechanism of antimony ion doping to optimize microwave dielectric properties of zinc zirconate tantalate ceramic

Herein, first-principles calculations predicted the atomic-scale variation of Sb5+ substitution for ZnZrTa2O8, and combined with the solid-phase reaction method to prepare ZnZr(Ta1-xSbx)2O8 (0.0 ≤ x ≤ 0.10) ceramics. ZnZr(Ta0.94Sb0.06)2O8 ceramics demonstrated the optimum microwave dielectric properties after sintering at 1350 °C for 6 h: εr = 24.92, Q × f = 134053 GHz (@7.18 GHz), and τf = −46.21 ppm/°C. For the non-intrinsic factors, the relative density increased from 96.54 % to 97.74 % and the average grain size increased from 19.88 μm to 21.85 μm, both of which reduced the dielectric loss. Regarding intrinsic factors, the progressive elevation of the Raman characteristic peak wave number and the heightened ionicity of Ta/Sb–O bonds predominantly account for the observed enhancement in εr. In addition, the attenuation of lattice vibrational damping behavior, the augmentation in electron cloud density, and the escalation of lattice energy collectively contribute to a decrement in dielectric loss. This study refines the examination of ionic substitution in ZnZrTa2O8 ceramics, offering theoretical insights for optimizing their dielectric properties and promoting their application in microwave communications.

Heat Bath in a Quantum Circuit.

We discuss the concept and realization of a heat bath in solid state quantum systems. We demonstrate that, unlike a true resistor, a finite one-dimensional Josephson junction array or analogously a transmission line with non-vanishing frequency spacing, commonly considered as a reservoir of a quantum circuit, does not strictly qualify as a Caldeira-Leggett type dissipative environment. We then consider a set of quantum two-level systems as a bath, which can be realized as a collection of qubits. We show that only a dense and wide distribution of energies of the two-level systems can secure long Poincare recurrence times characteristic of a proper heat bath. An alternative for this bath is a collection of harmonic oscillators, for instance, in the form of superconducting resonators.

Fractional particle and sigma model

We introduce a classical fractional particle model in ℝn, extending the Newtonian particle concept with the incorporation of the fractional Laplacian. A comprehensive discussion on kinetic properties, including linear momentum and kinetic energy, is provided. We further derive the equations of motion and discuss the symmetries of the system. The Green’s function method is employed to solve the equations of motion in a general case. We illustrate the theory with three important examples: the free fractional particle, the fractional harmonic oscillator, and the charged fractional particle that interacts locally with the electromagnetic field. We use the results of the extension problem by Caffarelli and Silvestre, to construct the associated classical local sigma model for the fractional particle. The sigma model is then quantized using the canonical quantization method, and we compute the vacuum energy at the boundary.